Traite de Logique by Edmond GoblotReview by: George SartonIsis, Vol. 3, No. 2 (Autumn, 1920), pp. 306-307Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/224030 .

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isis. III. 1920

Edmond Qoblot. - Traite de Logique. Preface de M. EMILE BOUTROUX.

xxII+412 p. Paris, Armand Colin, 1918.

Ce nouveau Traite de Logique merite d'8tre brievement analyse dans Isis non seulement a cause de son importance intrinseque, mais aussi a cause du parti que l'auteur a tire de l'etude de la pensee scientifique. I1 s'est efforce de construire une logique qui soit vraiment feconde, et et il a tres clairement vu que le seul moyen de rcussir etait de faire appel l'experience logique de l'humanite. I1 y insiste souvent: ( Ilest bon d'etudier ce que font, ce que disent et ce que pensent les savants; le logicien n'a point qualite pour les regenter; il doit au contraire se mettre a leur ecole et s'asseoir humblement sur le banc des etudiants. ) Un pareil traite de logique est aussi dans une certaine mesure un traite de psychologie, - une analyse de l'intelligence -, mais a vrai dire des qu'on sort du cadre etroit de la logique formelle, les frontieres de la logique deviennent tres difficiles a determiner. L'effort original d'EDMOND GOBLOT est digne des plus grands eloges. Notre seul reproche c'est qu'il n'ait pas fait un appel plus large encore a l'experience du passe. L'histoire de la science est une veritable mine d'experiences logiques, une mine qui est encore dans une large mesure inexploree. II est extraordinaire aussi que l'auteur n'ait point cru devoir tirer parti des travaux si suggestifs d'ERNST MACH.

Les idees fondamentales de ce livre sont les suivantes: Le raison- nement n'est pas essentiellement une analyse; il doit sa fecondite a des operations constructives (choix, rapprochement, combinaison, syn- these); il doit sa necessite i ce que toutes ces operations sont executees en vertu de regles; ces regles ne sont pas les regles de la logique, mais les propositions anterieurement admises; le role du syllogisme se borne a l'application de ces regles au cas considere. Le syllogisme hypothetique est seul fecond, le syllogisme categorique etant neces- sairement tautologique. II est impossible de concevoir un raison- nement independant des objets sur lesquels on raisonne.

Ce traite ne s'occupe aucunement des questions qui ressortissent a l'algebre de la logique et a la logistique. II ouvre une voie nouvelle, l'elaboration d'une logique experimentale et constructive, synthetique. I1 nous donne beaucoup a penser et a esperer. Car comme le rappelle BOUTROUX dans sa preface, la raison est susceptible de culture et de progres. Notre logique evolue, et c'est surtout le progres des sciences qui la fait evoluer.

Apres avoir entrepris des etudes medicales, poursuivies pendant quatre ans, EDMOND GOBLOT changea son dessein et devint docteur es lettres. Sa these de doctorat, Essai sur la classification des sciences (ALCAN, 1898) contient deja le germe des idees directrices de sa logique.

306

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On lui doit aussi un Vocabulaire Philosophique (Paris, COLIN) et Justice et Liberte (ALCAN, 1904; 2e ed., 1907). I1 est professeur d'histoire de la

philosophie et des sciences a l'Uniiversit6 de Lyon et correspondant de l'Institut. GEORGE SARTON.

M. J. M. Hill. - The Theory of Proportion, xx+108 p. London, CONSTABLE and C?., Ltd., 1914.

HILI maintains that a treatment of the theory of proportion, which

is valid when the magnitudes concerned are incommensurable, should be included in the mathematical curriculum. He has arrived at the conclusion that, in addition to the difficulties arising out of EUCLID's notation and out of the fact that EICLID did not sufficiently define

ratio, two reasons could be assigned for the great difficulty, of this argument: (1) Of the many definitions prefixed to the fifth Book, the only ones which effectively count are the fifth, the test for deciding when two ratios are equal, and the seventh, the test for distinguishing between unequal ratios. EUCLID has the logically unnecessary practice of deducing some of the properties of equal ratios from the seventh

definition. HILL merely uses the fifth for this purpose. (2) It seems

probable to HILL that the two assumptions: if A > B, then (A : C)

(B : C) were fundamental with EUCLID in the sense that he first deduced the fifth and seventh definitions from them and only afterwards reversed the process. The appearance of the above definitions at the beginning of EUCLID'S argument and without explanation presents grave difficulties to the student, which are avoided in this work. This work is a modification of EUCLID'S method, which requires for its understanding a knowledge of elementary algebra. The first three

chapters are devoted to an indication of what ( magnitudes of the same kind )) are (in essentials after SToIZ), some propositions on their

integral multiples, and the definition of the (( ratio)) of two such

multiples as a rational number. The (Chap. IV-V-XI) concept of ratio and number are extended so that irrational numbers are introduced, and Chap. VI-IX contain the theory of ratio of commensur- able and incommensurable magnitudes based on the above indications; the test for equal ratios is that no rational number lies between them.

Applications of STOLZ'S theorem simplifying this test are given in

Chap. X; and Chap. XII is a commentary on EUCLID'S fifth Book. J.

Smith, Major General, Sir F. - The Early History of Veterinary Lite-

rature and its British Development. Vol. 1, large in-8?, Iyl-373 p., 27 figures. London, BAILLIERE TINDALL and C?, 1919. [25/-]

This is the first attempt in English at a work on the History of

veterinary medicine and one of the fullest in any language. It is a

On lui doit aussi un Vocabulaire Philosophique (Paris, COLIN) et Justice et Liberte (ALCAN, 1904; 2e ed., 1907). I1 est professeur d'histoire de la

philosophie et des sciences a l'Uniiversit6 de Lyon et correspondant de l'Institut. GEORGE SARTON.

M. J. M. Hill. - The Theory of Proportion, xx+108 p. London, CONSTABLE and C?., Ltd., 1914.

HILI maintains that a treatment of the theory of proportion, which

is valid when the magnitudes concerned are incommensurable, should be included in the mathematical curriculum. He has arrived at the conclusion that, in addition to the difficulties arising out of EUCLID's notation and out of the fact that EICLID did not sufficiently define

ratio, two reasons could be assigned for the great difficulty, of this argument: (1) Of the many definitions prefixed to the fifth Book, the only ones which effectively count are the fifth, the test for deciding when two ratios are equal, and the seventh, the test for distinguishing between unequal ratios. EUCLID has the logically unnecessary practice of deducing some of the properties of equal ratios from the seventh

definition. HILL merely uses the fifth for this purpose. (2) It seems

probable to HILL that the two assumptions: if A > B, then (A : C)

(B : C) were fundamental with EUCLID in the sense that he first deduced the fifth and seventh definitions from them and only afterwards reversed the process. The appearance of the above definitions at the beginning of EUCLID'S argument and without explanation presents grave difficulties to the student, which are avoided in this work. This work is a modification of EUCLID'S method, which requires for its understanding a knowledge of elementary algebra. The first three

chapters are devoted to an indication of what ( magnitudes of the same kind )) are (in essentials after SToIZ), some propositions on their

integral multiples, and the definition of the (( ratio)) of two such

multiples as a rational number. The (Chap. IV-V-XI) concept of ratio and number are extended so that irrational numbers are introduced, and Chap. VI-IX contain the theory of ratio of commensur- able and incommensurable magnitudes based on the above indications; the test for equal ratios is that no rational number lies between them.

Applications of STOLZ'S theorem simplifying this test are given in

Chap. X; and Chap. XII is a commentary on EUCLID'S fifth Book. J.

Smith, Major General, Sir F. - The Early History of Veterinary Lite-

rature and its British Development. Vol. 1, large in-8?, Iyl-373 p., 27 figures. London, BAILLIERE TINDALL and C?, 1919. [25/-]

This is the first attempt in English at a work on the History of

veterinary medicine and one of the fullest in any language. It is a

On lui doit aussi un Vocabulaire Philosophique (Paris, COLIN) et Justice et Liberte (ALCAN, 1904; 2e ed., 1907). I1 est professeur d'histoire de la

philosophie et des sciences a l'Uniiversit6 de Lyon et correspondant de l'Institut. GEORGE SARTON.

M. J. M. Hill. - The Theory of Proportion, xx+108 p. London, CONSTABLE and C?., Ltd., 1914.

HILI maintains that a treatment of the theory of proportion, which

is valid when the magnitudes concerned are incommensurable, should be included in the mathematical curriculum. He has arrived at the conclusion that, in addition to the difficulties arising out of EUCLID's notation and out of the fact that EICLID did not sufficiently define

ratio, two reasons could be assigned for the great difficulty, of this argument: (1) Of the many definitions prefixed to the fifth Book, the only ones which effectively count are the fifth, the test for deciding when two ratios are equal, and the seventh, the test for distinguishing between unequal ratios. EUCLID has the logically unnecessary practice of deducing some of the properties of equal ratios from the seventh

definition. HILL merely uses the fifth for this purpose. (2) It seems

probable to HILL that the two assumptions: if A > B, then (A : C)

(B : C) were fundamental with EUCLID in the sense that he first deduced the fifth and seventh definitions from them and only afterwards reversed the process. The appearance of the above definitions at the beginning of EUCLID'S argument and without explanation presents grave difficulties to the student, which are avoided in this work. This work is a modification of EUCLID'S method, which requires for its understanding a knowledge of elementary algebra. The first three

chapters are devoted to an indication of what ( magnitudes of the same kind )) are (in essentials after SToIZ), some propositions on their

integral multiples, and the definition of the (( ratio)) of two such

multiples as a rational number. The (Chap. IV-V-XI) concept of ratio and number are extended so that irrational numbers are introduced, and Chap. VI-IX contain the theory of ratio of commensur- able and incommensurable magnitudes based on the above indications; the test for equal ratios is that no rational number lies between them.

Applications of STOLZ'S theorem simplifying this test are given in

Chap. X; and Chap. XII is a commentary on EUCLID'S fifth Book. J.

Smith, Major General, Sir F. - The Early History of Veterinary Lite-

rature and its British Development. Vol. 1, large in-8?, Iyl-373 p., 27 figures. London, BAILLIERE TINDALL and C?, 1919. [25/-]

This is the first attempt in English at a work on the History of

veterinary medicine and one of the fullest in any language. It is a

REVIEWS REVIEWS REVIEWS 307 307 307

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